In wavelength division multiplexed (WDM) optical communication systems, a number of different optical carrier wavelengths are separately modulated with data to produce modulated optical signals. The modulated signals are combined into an aggregate signal and transmitted over an optical transmission path to a receiver. The receiver detects and demodulates the data.
During transmission of the modulated signals over the transmission path, there are linear and non-linear impairments in the path. The linear impairments include chromatic dispersion (CD), polarization mode dispersion (PMD) and polarization dependent loss (PDL) and other similar effects. In general, chromatic dispersion is a differential delay in propagation of different wavelengths through the transmission path, and polarization mode dispersion is a differential delay in propagation of different polarizations through the transmission path. Polarization dependent loss is a differential attenuation for different polarizations through an optical path. The nonlinear impairments are related to nonlinear response of the transmission system and could be classified as self-phase modulation, cross-phase-modulation, four wave mixing (FWM) and other effects.
In phase modulated optical communication systems, e.g. systems using a phase-shift keying (PSK) or quadrature amplitude modulation (QAM) format, the receiver may be a coherent receiver using coherent detection, e.g. homodyne or heterodyne detection, to detect modulated optical signals. The term “coherent” when used herein in relation to a receiver refers to a receiver including a local oscillator (LO) for demodulating the received signal. Digital signal processing (DSP) may be implemented in such systems for processing the received signals to provide demodulated data. Digital signal processing of the received signal provides speed and flexibility, and may be used to perform a variety of functions including correction of nonlinearities associated with the optical transmission path such as chromatic dispersion, polarization mode dispersion, etc.
The DSP in the receiver may use an adaptive equalizer to recover transmitted information symbols from the received data. In one known example, an adaptive filter may be configured as a decision-directed adaptive linear filter. The filter may use a Least Mean Squares (LMS) estimation in which in which the coefficients Hkn for symbol n and tap k are adjusted based on the post-equalizer decision In and samples ykn asHkn+1=Hkn+μεnykn*,  (0)
where εn=In−ykn is the error signal and μ is a positive number small enough to ensure the convergence of the algorithm. The LMS estimation adjusts the filter coefficients to minimize the error signal εn. Other known adaptive filters may be configured as Recursive Least Squares (RLS) and Constant Modulus Algorithm (CMA), Multimodulus Algorithm (MMA) filters.
One known adaptive equalizer configuration using an RLS estimation of the signal after applying the back-propagation method is described in Inter-Channel Nonlinear Interference Noise in WDM Systems: Modeling and Mitigation Analysis of Polarization by R. Dar et al., published in the Journal of Lightwave Technology, vol. 33, No. 5, pp, 1044-1053, Mar. 1, 2015. Use of a back-propagation method may be effective but may be highly complex. Lower complexity versions may have limited capabilities in transmission paths that do not include chromatic dispersion compensation.